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Factorable Monoids
Resolutions and Homology via Discrete Morse Theory

dc.contributor.advisorBödigheimer, Carl-Friedrich
dc.contributor.authorHeß, Alexander
dc.date.accessioned2020-04-18T00:10:51Z
dc.date.available2020-04-18T00:10:51Z
dc.date.issued26.07.2012
dc.identifier.urihttp://hdl.handle.net/20.500.11811/5353
dc.description.abstractWe study groups and monoids that are equipped with an extra structure called factorability.
A factorable group can be thought of as a group G together with the choice of a generating set S and a particularly well-behaved normal form map G → S*, where S* denotes the free group over S. This is related to the theory of complete rewriting systems, collapsing schemes and discrete Morse theory.
Given a factorable monoid M, we construct new resolutions of Z over the monoid ring ZM. These resolutions are often considerably smaller than the bar resolution E*M.
As an example, we show that a large class of generalized Thompson groups and monoids fits into the framework of factorability and compute their homology groups. In particular, we provide a purely combinatorial way of computing the homology of Thompson's group F.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectGruppenhomologie
dc.subjectkombinatorische Gruppentheorie
dc.subjectdiskrete Morsetheorie
dc.subjectUmschreibsystem
dc.subjectNeuschreibsystem
dc.subjectTermersetzungssystem
dc.subjectThompsongruppe
dc.subjectFaktorabilität
dc.subjectfaktorable Gruppe
dc.subjectfaktorables Monoid
dc.subjectKollabierschema
dc.subjectgroup homology
dc.subjectcombinatorial group theory
dc.subjectdiscrete morse theory
dc.subjectrewriting system
dc.subjectthompson group
dc.subjectfactorability
dc.subjectfactorable group
dc.subjectfactorable monoid
dc.subjectcollapsing scheme
dc.subject.ddc510 Mathematik
dc.titleFactorable Monoids
dc.title.alternativeResolutions and Homology via Discrete Morse Theory
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-29325
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID2932
ulbbnediss.date.accepted2012-06-12
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeLück, Wolfgang


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